1176 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 8, APRIL 15, 2010 Efficient Design of Integrated Wideband Polarization Splitter/Combiner Mohamed A. Swillam, Member, IEEE, Mohamed H. Bakr, Member, IEEE, and Xun Li, Senior Member, IEEE Abstract—We propose a novel design of integrated polarization splitter/combiner with ultra wide bandwidth. The proposed de- sign utilizes the electro-optic (Pockels) effect in GaAs for splitting the polarizations. It also exploits the self imaging phenomenon in MMI couplers with a parabolic index distribution in the vertical direction to significantly increase the bandwidth. We also propose a novel approach for design optimization of the proposed structure. This approach is capable of extracting the propagation constants and their gradient with respect to all the design parameters. This allows for using gradient-based optimization. The computational time of this optimization procedure is only a fraction of that for other recently proposed approaches. Index Terms—Design optimization, electro-optic effect, modal analysis, multimode interference, polarization splitter, sensitivity analysis. I. INTRODUCTION P OLARIZATION splitters and combiners are essential op- tical components in optical communication systems. They are utilized for polarization diversity receivers [1]. They are also essential for polarization shift keying systems [2]. In the last few decades, various designs for polarization splitters have been pro- posed [3]–[7]. However, most of the proposed designs are only suitable for operation over a limited bandwidth. Designing an integrated polarization splitter with wideband operation is thus an essential requirement. Such a device will reduce the overall cost of the communication systems. In order to split the two light polarizations, the electro-optic effect can be utilized. This effect has been successfully applied in different designs [3], [4]. The bandwidth of these designs, however, is limited to few tens of nanometers. In order to increase the bandwidth, we propose a novel design of a polarization splitter. This design exploits the self imaging phenomenon in multimode interference (MMI) devices [8]. These devices enjoy wide bandwidth, ease of fabrication and integration, and fabrication tolerance. MMI devices have been Manuscript received September 14, 2009; revised November 25, 2009, January 04, 2010. First published March 04, 2010; current version published March 22, 2010. This work is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Discovery Grant RGPIN24978006. M. A. Swillam and M. H. Bakr are with the Computational Electromagnetics Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada. X. Li is with the Photonics Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada (e-mail: lixun@mcmaster.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2010.2043412 also utilized in many other applications. These applications include optical power splitters, combiners, optical hybrid cou- plers, multiplexers, and demultiplexers [8]–[16]. Recently, a design procedure for ultra wideband optical switching is proposed [17]. In this design, the self imaging in parabolic multimode index profile (PMMI) [18] is exploited to construct an optical switch with weak wavelength sensitivity. In order to reduce the complexity of the fabrication process of such a switch, a stair case refractive index with parabolic-like profile is utilized. To assure that this profile is capable of obtaining similar characteristics to those obtained using the parabolic profile, a two step optimization procedure is utilized. In this procedure, the beam propagation method (BPM) is ex- ploited to obtain the response. Even though the adjoint variable method is utilized to efficiently estimate the gradient of the response, the optimizer still requires a long computational time as it repeatedly calls the BPM to obtain the response and its gradient at each iteration. This overhead is mainly due to the long computational time of the BPM simulation. In this paper, we exploit the parabolic-like stair case index profile of a multimode interference (SCMMI) device to obtain an ultra wideband device that can work as a polarization splitter, combiner, and modulator. A novel design procedure is utilized for obtaining a new functionality of the parabolic-like MMI. This functionality is to split the polarization of the optical light over a wide band of wavelengths. The computational cost of obtaining the optimal design pa- rameters is reduced by using a one step optimization procedure. In this procedure, the wave equation is utilized to obtain the propagation constants of the profile. We also exploit an effi- cient approach to obtain the gradients (Jacobian) of the prop- agation constants with respect to all design parameters. A gra- dient-based optimization algorithm is then utilized to efficiently obtain the optimal design. The computational time of this novel procedure represents a small fraction of the procedure in [17]. We start by briefly describing the working principle of MMI as a polarization splitter using the electro-optic effect in Section II. In Section III, the novel procedure for designing the SCMMI is given. A design example and the characteristics of this device are given in Section IV. Finally, the conclusion of our work is given in Section V. II. MMI AS A POLARIZATION SPLITTER/COMBINER In this section, we propose a novel approach for utilizing the MMI as a polarization splitter. In this approach, the polariza- tion dependent electro-optic effect in the III-V semiconductors is exploited for actively splitting and modulating the TE and TM polarizations. An applied electric field in a specific lattice 0733-8724/$26.00 © 2010 IEEE